How to Calculate the Day of the Week for Any Date.

This example is here for demonstration purposes, not for you to figure out the code.

Days of the Week

var daysofweek = new Array('Sunday',
                                                'Monday',
                                                'Tuesday',
                                                'Wednesday',
                                                'Thursday',
                                                'Friday',
                                                'Saturday');

Calculating the day of the week

The following was taken from The Calendar FAQ.

To calculate the day on which a particular date falls, the following algorithm may be used (the divisions are integer divisions, in which the remainders are discarded):

a = (14 - month) / 12
y = year - a
m = month + 12 * a - 2
d = (day + y + y / 4 - y / 100 + y / 400 + (31 * m / 12) % 7

The value of d is 0 for a Sunday, 1 for a Monday, 2 for a Tuesday, etc.

This can be converted into the following simple script, where Math.floor converts floating point numbers to integers:

function DayOfWeek(day, month, year) {
    var a = Math.floor((14 - month) / 12);
    var y = year - a;
    var m = month + 12 * a - 2;
    var d = (day + y + Math.floor(y / 4) - Math.floor(y / 100) +
             Math.floor(y / 400) + Math.floor((31 * m) / 12))  % 7;
    return d;
}

Converting it to a named day

To test the function out, we'll find the day of the week that I was born on, by using the daysofweek[] array to display the day name:

document.write(daysofweek[DayOfWeek(4, 1, 1965) + 1]);

Which when run produces the following:

function DayOfWeek(day, month, year) {
    var a = Math.floor((14 - month) / 12);
    var y = year - a;
    var m = month + 12 * a - 2;
    var d = (day + y + Math.floor(y / 4) - Math.floor(y / 100) +
             Math.floor(y / 400) + Math.floor((31 * m) / 12))  % 7;
    return d + 1;
}

Now we would use the following to find out the day of the week of Christmas Day 1900:

document.write(daysofweek[DayOfWeek(25, 12, 1900)]);

Which when run produces the following:

The whole date and nothing but the date

With the addition of the monthsofyear[] array and the following two functions Nths() and FullDate() we can show the full information for a given date, e.g. Tuesday 28th October 1997.

var monthsofyear = new Array('January',
                                                  'February',
                                                  'March',
                                                  'April',
                                                  'May',
                                                  'June',
                                                  'July',
                                                  'August',
                                                  'September',
                                                  'October',
                                                  'November',
                                                  'December');

function Nths(day) {
    if (day == 1 || day == 21 || day == 31) return 'st';
    if (day == 2 || day == 22) return 'nd';
    if (day == 3 || day == 23) return 'rd';
    return 'th';
}

function FullDate(day, month, year) {
    return daysofweek[DayOfWeek(day, month, year)] + ' ' +
              day + Nths(day) + '  ' +  monthsofyear[month] + '  ' + year;
}

For example: document.write(FullDate(1, 1, 2000));

Which is the first day of the year 2000, returns: